Using DSP LLE all of them have a small audio delay. That was the case for every Dolphin rev. as far as I can remember.

Using DSP HLE both FE have a delay while both RE have perfect timing. However starting from AX HLE v2 merge both RE have a delay too.

So if HLE v2 is supposed to have a more precise audio processing and as a result all of my games have a delay using any audio backend is it correct that the delay is supposed to exist? Or is it just my games suffer from a bug and I should open an issue?

I am sensitive to such kind of things and I always play in headphones so I surely recognize a latency. But the latency is not that distractive so other people may very well not notice it. The observations above are correct for XAudio2, while DirectSound gives even a bit larger delay and OpenAL gives a horrible one (with latency=3 which is the fastest my X-Fi Titanium can handle without crackling).

Is my question just unimportant or no one has my games to test? I might try to pick some other games to test if that's the case. I'm pretty sure the latency doesn't exist on the actual Wii and it should be in the nature of Dolphin audio processing.